Non-collinear Magnetic Configurations at Finite Temperature in Thin Films

The finite-temperature magnetism of a monolayer on a bcc (110) surface was examined using a model Hamiltonian containing ferromagnetic or antiferromagnetic exchange interactions, Dzyaloshinsky-Moriya interactions and easy-axis on-site anisotropy. We examined the competition between the collinear ground state parallel to the easy axis and the spin spiral state in the plane perpendicular to this axis preferred by the Dzyaloshinsky-Moriya interaction. Using approximative methods to calculate the magnon spectrum at finite temperatures, it was found that even if the ground state is collinear, increasing the Dzyaloshinsky-Moriya interaction strongly decreases the critical temperature where this collinear order disappears. Using atomistic spin dynamics simulations it was found that at this critical temperature the system transforms into the non-collinear state. Including external magnetic field helps stabilising the ferromagnetic state. An effect due to the finite size of the magnetic monolayer was included in the model by considering a different value for the anisotropy at the edges of the monolayer. This effect was shown to stabilize the spin spiral state by fixing the phase at the ends of the stripe.

Langevin spin dynamics based on ab initio calculations: numerical schemes and applications

A method is proposed to study the finite-temperature behaviour of small magnetic clusters based on solving the stochastic Landau-Lifshitz-Gilbert equations, where the effective magnetic field is calculated directly during the solution of the dynamical equations from first principles instead of relying on an effective spin Hamiltonian. Different numerical solvers are discussed in the case of a one-dimensional Heisenberg chain with nearest-neighbour interactions. We performed detailed investigations for a monatomic chain of ten Co atoms on top of Au(001) surface. We found a spiral-like ground state of the spins due to Dzyaloshinsky-Moriya interactions, while the finite-temperature magnetic behaviour of the system was well described by a nearest-neighbour Heisenberg model including easy-axis anisotropy.

Relativistic and thermal effects on the magnon spectrum of a ferromagnetic monolayer

A spin model including magnetic anisotropy terms and Dzyaloshinsky-Moriya interactions is studied for the case of a ferromagnetic monolayer with C2v symmetry like Fe/W(110). Using the quasiclassical stochastic Landau-Lifshitz-Gilbert equations, the magnon spectrum of the system is derived using linear response theory. The Dzyaloshinsky-Moriya interaction leads to asymmetry in the spectrum, while the anisotropy terms induce a gap. It is shown that in the presence of lattice defects, both the Dzyaloshinsky-Moriya interactions and the two-site anisotropy lead to a softening of the magnon energies. Two methods are developed to investigate the magnon spectrum at finite temperatures. The theoretical results are compared to atomistic spin dynamics simulations and a good agreement is found between them.

Exchange Bias driven by Dzyaloshinskii-Moriya interactions

The exchange bias effect in compensated IrMn3/Co(111) system is studied using multiscale modeling from ab initio to atomistic calculations. We evaluate numerically the out-of-plane hysteresis loops of the bi-layer for different thickness of the ferromagnetic layer. The results show the existence of a perpendicular exchange bias field and an enhancement of the coercivity of the system. In order to elucidate the possible origin of the exchange bias, we analyze the hysteresis loops of a selected bi-layer by tuning the different contributions to the exchange interactions across the interface. Our results indicate that the exchange bias is primarily induced by the Dzyaloshinskii-Moriya interactions, while the coercivity is increased mainly due to a spin-flop mechanism.

Atomistic spin-model based on a new spin-cluster expansion technique: Application to the IrMn3/Co interface

In order to derive tensorial exchange interactions and local magnetic anisotropies in itinerant magnetic systems, an approach combining the Spin-Cluster Expansion with the Relativistic Disordered Local Moment scheme is introduced. The theoretical background and computational aspects of the method are described in detail. The exchange interactions and site resolved anisotropy contributions for the IrMn3/Co(111) interface, a prototype for an exchange bias system, are calculated including a large number of magnetic sites from both the antiferromagnet and ferromagnet. Our calculations reveal that the coupling between the two subsystems is fairly limited to the vicinity of the interface. The magnetic anisotropy of the interface system is discussed, including effects of the Dzyaloshinskii-Moriya interactions that appear due to symmetry breaking at the interface.

The exchange coupling between the valence electrons of the fullerene cage and the electrons of the N atoms in N@C60^{-1,3}

MCSCF calculations are performed in order to determine the exchange coupling between the 2p electrons of the N atom and the LUMOs of the fullerene cage in the case of mono- and tri-anions of N@C60. The exchange coupling resulted by our calculations is large compared to the hyperfine interaction. The strong coupling can explain the missing EPR signal of the nitrogen in paramagnetic anions.

Chiral asymmetry of the spin-wave spectra in ultrathin magnetic films

We raise the possibility that the chiral degeneracy of the magnons in ultrathin films can be lifted due to the presence of Dzyaloshinskii-Moriya interactions. By using simple symmetry arguments, we discuss under which conditions such a chiral asymmetry occurs. We then perform relativistic first principles calculations for an Fe monolayer on W(110) and explicitly reveal the asymmetry of the spin-wave spectrum in case of wave-vectors parallel to the (001) direction. Furthermore, we quantitatively interpret our results in terms of a simplified spin-model by using calculated Dzyaloshinskii-Moriya vectors. Our theoretical prediction should inspire experiments to explore the asymmetry of spin-waves, with a particular emphasis on the possibility to measure the Dzyaloshinskii-Moriya interactions in ultrathin films.

Giant magnetic anisotropy of the bulk antiferromagnets IrMn and IrMn3

Theoretical predictions of the magnetic anisotropy of antiferromagnetic materials are demanding due to a lack of experimental techniques which are capable of a direct measurement of this quantity. At the same time it is highly significant due to the use of antiferromagnetic components in magneto-resistive sensor devices where the stability of the antiferromagnet is of upmost relevance. We perform an ab-initio study of the ordered phases of IrMn and IrMn3, the most widely used industrial antiferromagnets. Calculating the form and the strength of the magnetic anisotropy allows the construction of an effective spin model, which is tested against experimental measurements regarding the magnetic ground state and the Neel temperature. Our most important result is the extremely strong second order anisotropy for IrMn3 appearing in its frustrated triangular magnetic ground state, a surprising fact since the ordered L12 phase has a cubic symmetry. We explain this large anisotropy by the fact that cubic symmetry is locally broken for each of the three Mn sub-lattices.

First principles calculation of spin-interactions and magnetic ground states of Cr trimers on Au(111)

We present calculations of the magnetic ground states of Cr trimers in different geometries on top of a Au(111) surface. By using a least square fit method based on a fully relativistic embedded-cluster Greens function method first we determined the parameters of a classical vector-spin model consisting of second and fourth order interactions. The newly developed method requires no symmetry constraints, therefore, it is throughout applicable for small nanoparticles of arbitrary geometry. The magnetic ground states were then found by solving the Landau-Lifshitz-Gilbert equations. In all considered cases the configurational energy of the Cr trimers is dominated by large antiferromagnetic nearest neighbor interactions, whilst biquadratic spin-interactions have the second largest contributions to the energy. We find that an equilateral Cr trimer exhibits a frustrated 120$^circ$ Neel type of ground state with a small out-of-plane component of the magnetization and we show that the Dzyaloshinsky-Moriya interactions determine the chirality of the magnetic ground state. In cases of a linear chain and an isosceles trimer collinear antiferromagnetic ground states are obtained with a magnetization lying parallel to the surface.